Mixing instabilities during shearing in metals

The dynamics of deformation during shearing in metallic multilayers have been captured using 3D X-ray synchrotron tomography. The observations include the formation of folds and vortices and delamination of layers. Numerical simulations show that metals behave as very viscous fluids. The process is similar to rock folding in geology.

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We tend to think of common metals as rigid solids. This perspective is challenged here as new evidence shows that metals behave as very viscous fluids when subjected to shear deformation even at room temperature.

Interestingly, geologists already knew for quite a while that many large-scale geodynamical deformations taking place within the Earth over millions of years can be shown to follow fluidic behaviour. Indeed, they have been successfully using such an approach to explain phenomena such as rock folding and mountain building. Now, it has been demonstrated that such behaviour is not restricted to large dimensions and durations. In fact, even during short-period deformations and at the micrometre scale, metals behave similarly.

These findings were made possible by a novel experimental strategy that has enabled the morphological evolution within deforming solids to be captured in three dimensions for the first time. For this purpose, multilayers of copper/silver and copper/aluminium, representing a multiphase alloy, were created by alternately stacking individual 25-μm-thick foils of each material. Next, the multilayers were shear deformed using the high-pressure torsion (HPT) method (Figure 1a), whereby the sample is squeezed between two anvils while one anvil is rotating. This results in the formation of a disk-like sample.

Figure 1. (a) Schematic drawing showing the high-pressure torsion (HPT) setup and a multilayer sample placed between the anvils of the apparatus. The process applies a shear stress parallel to the layers and results in the formation of a disk-shaped sample. (b) A parallelepiped-shaped volume section, cut out of the processed disk and subsequently imaged by 3D X-ray synchrotron tomography. The tomographic images show selected cross-sections of the volume element, cut at different distances from the centre of the disk, with (I) representing the centre (and thus having experienced the lowest strain) and (V) typifying the microstructure at the edge of the disk (and thus having been subjected to the highest strain).

During high-pressure torsion, each radial cross-section (i.e., plane with radius as its normal) is sheared to a slightly different extent due to the existence of a strain gradient along the radius of the disk. This causes a gradual evolution of morphology in the multilayer from its original phase-separated state to a relatively mixed-phase state, in the resulting sample disk. The interfacial and morphological evolution undergone by the stack could then be discovered by looking at successive cross-sections at different radii, corresponding to different levels of strain, using 3D X-ray synchrotron tomography at beamline ID19 (Figure 1b). This technique revealed a host of morphological events including delamination of the layers, formation of folds and rotating vortices in the multilayers (Figure 2), which were not considered in the previous atomic-scale mixing studies (e.g. [1]).

Figure 2. Morphological evolution of multilayers upon shearing acquired by 3D X-ray synchrotron tomography. (a–e) Selected snapshots of an Ag/Cu-multilayer that has been shear-deformed to a maximum strain of 393. The brighter phases are Ag. Here, the Cu layers predominantly delaminate before mixing takes place at the micrometre scale. (f–j) Selected snapshots of an Al/Cu-multilayer, shear-deformed to a maximum strain of 236. The brighter phases are Cu. Here, the Cu layers initially fold in a quasi-regular manner and subsequently evolve into periodic vortices, before mixing takes place at the micrometre scale. Note that in both sequences, the overall strain increases when going from the top to the bottom of each panel. The scale bar is 200 μm. The dark area within (e) is a crack that appeared after HPT deformation and during the cutting of the disk for tomography examination. See also: videos of morphological evolution during shearing: 1. in Ag/Cu, corresponding to (a-e) and 2) in Al/Cu, corresponding to (f-j).

These new observations resembled many similarities to morphologies found in rocks. Hence, a computer model that was originally designed for mountain building processes was adapted to simulate the experimental conditions. The model identified the viscosity contrast (VC) and the stress exponent of the phases (n), as well as the strain rate (˙γ) as the key factors driving the microstructural evolution. Figure 3 shows the results of a simulation for a particular combination of (VC, n). In short, the results indicate that the same instability that causes kilometre-thick rock layers to fold on geological timescales is acting here at micrometre level.

Figure 3. Finite element simulation of shear deformation in a multilayer system. (a) The computational cell showing the initial arrangement of the layers and the direction of shear at the top. Black (lower characteristic viscosity) and white (higher characteristic viscosity) layers denote the two different phases in each experiment, and the model domain is comparable in size to that of the samples used in 3D X-ray synchrotron tomography experiments. (b–g) Simulation results for (VC = 10, n = 3). (b–d) Local strain rate (˙γII), effective viscosity (ηeff), and morphology maps at shear strain γ = 10, respectively. The arrows in (d) point to two folding layers. (e–g) Evolution of morphology with the increase of shear strain (γ) as indicated.

The findings reveal the origin for the emergence of a wealth of morphologies in deforming solids. While the experiments were performed on multilayers under shear, the model is not limited to samples of this type and could be applied to any material system regardless of its morphology. This makes the model a versatile tool to study a broad range of materials and material processing techniques.